What is the integral of x^2e^{9x} ?

The integral of x^2e^{9x} is 1/9 e^{9x}x^2-2/729 (9e^{9x}x-e^{9x})+C

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integral of x^2e^{9x}

\int x^{2} e^{9 x} d x

\frac{1}{9} e^{9 x} x^{2} - \frac{2}{729} (9 e^{9 x} x - e^{9 x}) + C

Solution steps

\int x^{2} e^{9 x} d x

Apply Integration By Parts

: \frac{1}{9} e^{9 x} x^{2} - \int \frac{2}{9} e^{9 x} x d x

= \frac{1}{9} e^{9 x} x^{2} - \int \frac{2}{9} e^{9 x} x d x

\int \frac{2}{9} e^{9 x} x d x = \frac{2}{729} (9 e^{9 x} x - e^{9 x})

= \frac{1}{9} e^{9 x} x^{2} - \frac{2}{729} (9 e^{9 x} x - e^{9 x})

Add a constant to the solution

= \frac{1}{9} e^{9 x} x^{2} - \frac{2}{729} (9 e^{9 x} x - e^{9 x}) + C

\frac{d}{d x} (x^{4} + 8)

x \to - \infty lim (5 + x^{2})

\frac{d y}{d x} = x y

y^{^{''}} + 4 y + 8 = 0, y (0) = 4, y^{^{'}} (0) = - 3

f (x) = - 2 \cdot x, at x = 1

What is the integral of x^2e^{9x} ?
The integral of x^2e^{9x} is 1/9 e^{9x}x^2-2/729 (9e^{9x}x-e^{9x})+C